Module for the Mechanical Uncoupling of a Resonator Having a High Quality Factor

ABSTRACT

The device ( 10 ) comprises a cylindrical resonator (R) vibrating in extension-compression along its longitudinal axis (Δ) and having a vibration node (N) in its mid-plane (π), the vibration naturally generating radial extension/compression deformations, and a mechanical decoupling module comprising a hollow cylinder ( 2 ) surrounding the resonator and a membrane ( 1 ) positioned in the aforementioned mid-plane and rigidly connected to the cylindrical surface of the resonator and to the internal cylindrical surface of the hollow cylinder. The hollow cylinder vibrates in extension/compression in antiphase with the vibration of the resonator, enabling the effects of the radial deformations of the hollow cylinder and of the resonator to compensate each other in an area (ZF) located on the external surface of the hollow cylinder close to the mid-plane.

The invention relates to the field of mechanical resonators used forconstructing instruments for measuring time or frequency.

More specifically, the invention relates to a module for the mechanicaldecoupling of a resonator having a high quality factor, intended for usein highly stable clocks called “ultra-stable oscillators” (USOs).

A USO is composed of a mechanical resonator of this type and anelectronic oscillator circuit which enables the vibration of theresonator to be kept at its mechanical resonance frequency. Thus thestability of the frequency of the alternating electrical signal presentin the electronic circuit benefits from the stability of the frequencyof the mechanical resonance of the resonator, which is generally muchgreater than that of a purely electronic oscillator circuit.

The stability of the resonant frequency of the mechanical resonatorincreases with the quality factor of the resonant vibration; in otherwords, the vibration energy contained in the resonator is large relativeto the energy lost per vibration period. There are two types of energyloss, which are, on the one hand, the intrinsic losses, due for exampleto the viscous damping of the material from which the resonator is made,and, on the other hand, the extrinsic losses due to gas damping or tounsuitable fixing of the resonator, for example. Because of this, thebest resonators are made from materials having very low viscous damping,such as quartz; they are also packaged in casings in a vacuum, and areattached in each casing at a location which is referred to by theaccepted theoretical term “vibration node”.

There is a practical formulation for expressing the contribution of thedifferent sources of energy loss, as explained below.

The expression for the actual quality factor of the resonator is writtenthus:

Q actual=2π·E/ΔE

where E is the energy contained in the resonator and ΔE is the energylost per vibration period. For the aforementioned examples, ΔE can bewritten thus:

ΔE=ΔE intrinsic+ΔE gas+ΔE attachment

Therefore we can write:

1/Q actual=(ΔE intrinsic+ΔE gas+ΔE attachment)/2π·E

Therefore,

1/Q actual=ΔE intrinsic/2π·E+ΔE gas/2π·E+ΔE attachment/2π·E

Thus we can associate each source of energy losses with its own qualityfactor, and we can write:

1/Q actual=1/Q intrinsic+1/Q gas+1/Q attachment

In order for the actual quality factor of the resonator to be close toits intrinsic quality factor, therefore, the quality factors associatedwith the various sources of extrinsic losses must be much greater thanthe intrinsic quality factor. For example, if Q intrinsic is about 10⁶,Q attachment and Q gas are preferably at least 10⁷ or thereabouts.

The invention relates in particular to the losses caused by theattachment of the resonator, and is intended to ensure that Q attachmentis much greater than Q intrinsic.

The attachment of a resonator at the location of a vibration node is aconcept which is easily understood in the textbook case of a pointattachment and a resonator model having a single spatial dimension.However, in the real case of a resonator in three dimensions, to belocated in an attachment area which inevitably has non-zero dimensions,the problem is generally difficult to resolve, and requires the use of amechanical decoupling module. This mechanical decoupling module is anintegral part of a device incorporating the resonator. It must be madefrom a material with very low viscous damping and must allow the deviceto have an area which is sufficiently decoupled from the mechanicalvibration of the resonator. Thus, the attachment of this area in thecasing does not adversely affect the quality factor of the resonator.This attachment area can be considered as a vibration node of thedevice. Evidently, a higher intrinsic quality of the resonator willrequire a greater efficiency of the decoupling module.

For resonators with high quality factors to be used in USOs, there is aknown way of making a device which is monolithic, is formed by a quartzblank vibrating in thickness-shear mode, and is attached at its edge(U.S. Pat. No. 4,381,471). One face of the blank is flat and the otherface is convex, such that the vibration energy is located primarily inthe central region of the blank (the thickest region) and fadesprogressively until it disappears completely at the edge. Thus thecentral region of the blank can be considered to be the resonator, withthe edge forming the attachment area, and the rest of the blank beingthe mechanical decoupling module. Metal electrodes deposited on the mainfaces of the blank in the central region are used to excite thevibration of the resonator by a piezoelectric effect. It should be notedthat this device also operates in thickness extension/compression mode,according to the same operating principle of the mechanical decouplingresulting from the convexity of one of the faces of the blank.

This known prior art device operates remarkably well because it providesmechanical decoupling which is effective enough to prevent anyalteration of the high intrinsic quality factor of the resonator. Thisknown device is generally attached by means of metal supports, eachhaving one end mounted on the edge of the blank and the other endmounted on a sealed cross-piece of the casing, thus facilitating theelectrical connection between the sealed cross-pieces of the casing andthe metal electrodes deposited on the blank.

There is also a known way of removing material near the edge of theblank so that the device has a peripheral ring connected by links to acentral blank which is smaller than the original blank, and reducing thethickness of these links in the dimension of the thickness of the blank(Patent FR 2 338 607 or its equivalent U.S. Pat. No. 4,135,108). Thisdevice is attached by its peripheral ring, thus protecting the centralblank from parasitic effects, due for example to heat or to the presenceof an acceleration field. On the other hand, the ring and links make nocontribution to the mechanical decoupling of the vibration of theresonator, since the mechanical decoupling is again provided by theconvexity of one of the faces of the blank.

However, these known devices have a drawback in that it is difficult toform the convex face of the blank with sufficient precision, notably asregards conformity with the precise value of the optimal radius ofcurvature. Because of this requirement, therefore, each blank producedmust be subjected to an inspection and refinishing procedure, resultingin high manufacturing costs.

The object of the invention is, notably, to overcome the drawbacks ofthe prior art by proposing a device including a mechanical decouplingmodule which is equally effective but can be produced by an inexpensivemachining process.

To this end, the device including a resonator and a mechanicaldecoupling module, in which the resonator is formed by a right cylindervibrating in extension/compression mode along its central longitudinalaxis and having a vibration node in its mid-plane which is perpendicularto the longitudinal axis, and in which the vibration naturally inducesradial extension/compression deformations, is characterized in that thedecoupling module includes a hollow right cylinder surrounding andspaced apart from the resonator and having its central longitudinal axisand its mid-plane coinciding with those of the resonator, and a membranepositioned in the mid-plane and rigidly connected to the cylindricalsurface of the resonator and with the internal cylindrical surface ofthe hollow cylinder, and in that the hollow cylinder vibrates in anextension/compression mode along its longitudinal axis in antiphase withthe vibration of the resonator, as a result of which the effects of theradial deformations of the hollow cylinder and of the resonatorcompensate each other in an area located on the external surface of thehollow cylinder close to the mid-plane.

The simultaneous vibrations in antiphase of the resonator and of thehollow cylinder correspond to a specific mechanical resonance mode ofthe device according to the invention, a condition of the existence ofthis mode being that the heights of the resonator and the hollowcylinder are substantially the same.

Thus, the aforesaid area located on the external surface of the hollowcylinder may be decoupled from the vibration of the resonator, and byattaching the device to this area the actual quality factor of theresonator may be brought close to its high intrinsic quality factor. Inorder to achieve maximum decoupling, the design of the device isoptimized, for example by digital simulation based on the finite elementmethod.

The device may also be formed from a flat plate of material in which thethickness dimension lies on the longitudinal axis of the resonator, bymeans of inexpensive machining carried out on both faces of the plate toprovide a depth corresponding to the membrane. For example, the deviceis formed by combined chemical machining of a quartz plate by a methodsimilar to that used in the clockmaking industry for manufacturingquartz crystals for watches.

The features and advantages of the invention will become clear from thedetailed description and the drawings relating thereto, in which:

FIG. 1A is a perspective view of a monolithic device according to afirst embodiment of the invention, suitable for an isotropic material;

FIG. 1B is a perspective view in longitudinal section of the device ofFIG. 1A;

FIGS. 2A and 2B show exaggeratedly magnified deformations of thevibrating resonator, to illustrate how the extension/compressionvibration of the resonator along its longitudinal axis naturally inducesradial extension/compression deformations called Poisson effects;

FIG. 3A is a view similar to FIG. 1A, showing the attachment area of thedevice;

FIG. 3B is a view similar to FIG. 1B, showing the longitudinal movementsof the resonator and of the hollow cylinder, together with theassociated Poisson effects;

FIG. 4 shows a way of holding the device of FIG. 3A, using metalsupports;

FIGS. 5A and 5B show a way of holding the device of FIG. 3A, using anintegrated attachment system;

FIGS. 6A and 6B show a monolithic device according to a secondembodiment of the invention, comprising an additional hollow cylindersurrounding and spaced apart from the aforesaid hollow cylinder andintended to enable the effectiveness of the mechanical decoupling moduleto be maintained with higher manufacturing tolerances;

FIGS. 7A and 7B show a monolithic device according to a third embodimentof the invention, suitable for quartz; and

FIGS. 8A and 8B show a non-monolithic device according to a fourthembodiment of the invention, suitable for silicon.

Reference will be made initially to FIG. 1A, which shows a perspectiveview of a device 10 according to the invention, and to FIG. 1B whichshows a perspective view in longitudinal section of FIG. 1A. The device10 includes a resonator R formed by a right cylinder with a circulardirectrix and a central longitudinal axis 4, which is symmetrical abouta mid-plane n perpendicular to the longitudinal axis; a right hollowcylinder 2 with circular directrices, surrounding and spaced apart fromthe resonator and having its central longitudinal axis and its mid-planecoinciding with those of the resonator; and a membrane 1 positioned inthe aforementioned mid-plane and rigidly connected to the cylindricalsurface of the resonator and to the internal cylindrical surface of thehollow cylinder.

The hollow cylinder 2 and the membrane 1 form the mechanical decouplingmodule of the device 10.

In the illustration, the resonator R and the hollow cylinder 2 have thesame height dimension h. It is important for the operation of the devicethat the resonator R and the hollow cylinder 2 have substantially thesame height, as explained below.

The symbol Φ denotes the diameter of the resonator R; d1 and e denote,respectively, the radial dimension and thickness of the membrane 1; andd2 denotes the thickness of the wall of the hollow cylinder 2, in otherwords the difference between its external radius and its internalradius.

The device 10 is monolithic and is made from a flat plate of isotropicmaterial having very low viscous damping, such as silica. The thicknessdimension of the plate lies on the longitudinal axis Δ of the resonatorand is equal to the aforesaid height h. The device 10 is formed, forexample, by plasma machining on both faces of the plate, until a depthcorresponding to the membrane is reached.

The operation of the device according to the invention will now beexplained with reference to FIGS. 2A, 2B, 3A and 3B.

FIGS. 2A and 2B are views in longitudinal section of the resonator R andthe membrane 1 of FIG. 1B, and show exaggeratedly magnified deformationsof the resonator vibrating alternately in extension (FIG. 2A) and incompression (FIG. 2B) along its longitudinal axis A and having avibration node N in its mid-plane n. The extension/compression vibrationnaturally induces radial extension/compression deformations due to thePoisson coefficient of the material, these radial deformations beingmaximal in the mid-plane n and zero at the ends of the resonator. Thusthe vibration of the resonator has only one vibration node (N) locatedon the longitudinal axis A, in other words at the core of the resonatormaterial. In these drawings, the longitudinal deformations are indicatedby vector arrows and the radial deformations are indicated by V-shapedarrows.

To ensure that the extension/compression vibration of the resonatoralong its longitudinal axis is sufficiently pure, or in other words thatthe cross sections of the resonator undergo, for practical purposes,only the aforementioned longitudinal translations and radialdeformations, the height h of the resonator must be markedly greaterthan its diameter Φ. Preferably, the height h is between three times andten times the diameter Φ.

The positioning of the membrane 1 in the mid-plane n is advantageous inrespect of the deformations of the resonator along its longitudinalaxis, because it allows the membrane to remain in the mid-plane duringthe vibration of the resonator, but the radial alternating extension andcompression deformations of the resonator in the mid-plane π actdirectly on the membrane 1 and cause, in particular, alternatingvariations of its external diameter.

In other words, it would not be advantageous for the membrane 1 to beattached directly in the casing, because this would lead to losses ofthe vibration energy of the resonator. However, the positioning of themembrane 1 in the mid-plane n can be considered to be a major advantagein respect of the mechanical decoupling of the vibration of theresonator. It should be noted that this remark is meaningful only if thethickness e of the membrane is sufficiently small with respect to theheight h of the resonator. Preferably, the thickness e is less than atwentieth of the height h. It is also important for the radial dimensiond1 of the membrane not to be too large with respect to its thickness e,in order to ensure that parasitic modes of mechanical resonance of themembrane do not disturb the operation of the device according to theinvention. Preferably, the dimension d1 is not more than twenty timesthe thickness e.

With reference to FIGS. 3B and 3A, it will now be explained how thehollow cylinder 2 surrounding the resonator R can provide excellentmechanical decoupling of the vibration of the resonator. FIG. 3B is aview similar to FIG. 1B, in which arrows are used to indicate thelongitudinal deformations of the resonator and of the hollow cylinder 2,together with the associated radial deformations, when the resonator Ris in resonant vibration. The arrows corresponding to the hollowcylinder are shown in broken lines. The hollow cylinder vibrates in anextension/compression mode along its longitudinal axis in antiphase withthe vibration of the resonator. It must be emphasized that thesimultaneous vibrations in antiphase of the resonator and of the hollowcylinder correspond to a specific mechanical resonance mode of thedevice according to the invention, acting in a rather similar way to thesimultaneous vibrations in antiphase of the two substantially identicalprongs of a tuning fork in resonant vibration. For the device accordingto the invention, a condition of the existence of the specific resonancemode is that the heights of the resonator R and the hollow cylinder 2are substantially the same, as a result of which the resonantextension/compression vibrations of the resonator and of the hollowcylinder considered separately have similar frequencies. If thiscondition is met, the membrane 1 rigidly connected to these two elementsprovides strong mechanical coupling between their vibrations, rather asdoes the base rigidly connected to the two prongs of a tuning fork, thusenabling the aforesaid specific resonance mode to exist.

Whereas the two substantially identical prongs of a tuning fork havesubstantially identical amplitudes of vibration, the amplitudes ofvibration of the resonator R and of the hollow cylinder 2 of the deviceaccording to the invention are generally very different from each other,because the mass of the hollow cylinder is generally much greater thanthat of the resonator. Consequently the amplitude of vibration of thehollow cylinder is generally very much lower than that of the resonator,thereby naturally balancing the quantities of movement present in thespecific resonance mode of the device according to the invention. Thereader will have noted that the radial dimensions of the hollowcylinder, particularly its wall thickness d2, are dimensional parameterswhich can be used to adjust the ratio between the amplitude of vibrationof the hollow cylinder and that of the resonator to a certain extent,without affecting the existence of the specific resonance mode of thedevice. This freedom of action is exploited profitably in the deviceaccording to the invention, as explained below.

With reference to FIG. 3B again, the longitudinal deformations of thehollow cylinder induce radial deformations of its wall. More precisely,a longitudinal extension induces a compression of the wall thickness d2,and a longitudinal compression induces an extension of the thickness d2.In both cases, this causes opposing radial movements on the external andinternal cylindrical surfaces of the hollow cylinder respectively,making it possible to obtain two specific qualities of the deviceaccording to the invention.

The first quality is due to the fact that the radial movements of theinternal cylindrical surface of the hollow cylinder are in the samedirection as those of the cylindrical surface of the resonator, whichcontributes to the creation, through the intermediary of the membrane 1,of the aforesaid strong mechanical coupling between the vibrations ofthe resonator and those of the hollow cylinder.

The second quality of the device according to the invention is due tothe fact that, on the external cylindrical surface of the hollowcylinder, the radial movements due to the radial deformations of thehollow cylinder are in the opposite direction to those due to the radialdeformations of the resonator, thus enabling their effects to becompensated in an area located on the external surface of the hollowcylinder close to the mid-plane n. Thus, the aforesaid area may bevirtually decoupled from the vibration of the resonator, and byattaching the device to this area the actual quality factor of theresonator may be brought close to its high intrinsic quality factor.This area, called the attachment area, is denoted ZF and is delimited bybroken lines in FIG. 3A. The attachment area ZF is a cylindrical surfacewith a height z, having the same mid-plane (n) as the resonator and thehollow cylinder. The height z is generally greater than the thickness eof the membrane 1. For example, the height z may be equal to twice thethickness e, which is relatively convenient for the positioning of anattachment system on the area ZF, as described below. In order toachieve maximum decoupling of the area ZF in respect of the vibration ofthe resonator, the design of the device according to the invention isoptimized, for example by means of digital simulations based on thefinite element method. The Poisson effects due to the hollow cylinderand to the resonator may be compensated virtually entirely by adjustingthe longitudinal amplitude of vibration of the hollow cylinder, sincethe Poisson effects due to the hollow cylinder are proportional to thisamplitude. As mentioned above, this adjustment can be carried out byvarying the mass of the hollow cylinder, for example by varying its wallthickness d2. In the illustration, the radial dimension d2 is of thesame order of magnitude as the diameter Φ of the resonator. Moregenerally, the radial dimension d2 is preferably between half thediameter Φ and twice the diameter Φ.

We have now explained the mechanism by which, when using a resonator Rhaving a single vibration node N in the core of its material, thedecoupling module, including a membrane 1 and a right hollow cylinder 2,enables the device 10 according to the invention to have an attachmentarea ZF which is virtually decoupled from the vibration of the resonatorand is located on the external cylindrical surface of the hollowcylinder, thereby being easily accessible for positioning a system forattaching the device in a casing. This attachment system may havevarious configurations.

For example, FIG. 4 shows an attachment system in the form of metalsupports SM, each having one end mounted on the attachment area ZF andthe other end mounted on a base of the casing EB (not shown), accordingto the procedure used in the prior art explained in the preamble.

Also by way of example, FIGS. 5A and 5B show an attachment systemintegrated in the device 10 according to the invention, the mountingtaking place in the same flat plate of material. The attachment systemcomprises a right hollow cylinder CC with substantially squaredirectrices, surrounding and spaced apart from the hollow cylinder 2,and links of reduced thickness P positioned in the mid-plane n andrigidly connected to the external cylindrical surface of the hollowcylinder 2 and to the internal cylindrical surface of the hollowcylinder CC. One of the external bases of the hollow cylinder CC ismounted on a base of the casing EB (not shown). This attachment systemis thus related to that used in the prior art explained in the preamble,and may be useful in that it protects the device 10 according to theinvention from parasitic effects, due for example to heat or to thepresence of an acceleration field. However, the hollow cylinder CC andthe links P make no contribution to the mechanical decoupling of thevibration of the resonator. The shape of the hollow cylinder CC istherefore of little importance, and may, for example, be modelled onthat of the base of the casing EB.

Reference will now be made to FIGS. 6A and 6B which show a device 20according to a second embodiment of the invention. The device 20comprises the aforesaid device 10; an additional right hollow cylinder 4surrounding and spaced apart from the hollow cylinder 2 and having itscentral longitudinal axis and its mid-plane coinciding with those of thedevice 10; and an additional membrane 3 positioned in the aforementionedmid-plane and rigidly connected to the external cylindrical surface ofthe hollow cylinder 2 and to the internal cylindrical surface of theadditional hollow cylinder 4.

The use of the device 20 may be helpful, for example if widermanufacturing tolerances are required.

The device 20 has a specific resonance mode for which the hollowcylinder 2 and the resonator R vibrate in antiphase with each other asexplained above for the device 10, and the additional hollow cylinder 4vibrates in antiphase with the hollow cylinder 2. Thus any residualradial movements which remain on the external surface of the hollowcylinder 2 close to the mid-plane, due to manufacturing defects forexample, have their effects compensated by the radial deformations ofthe additional hollow cylinder 4 in an attachment area ZF′ located onthe external cylindrical surface of the additional hollow cylinder 4close to the mid-plane, by the same mechanism as that explained for thedevice 10. The decoupling module of the device 20 can therefore beconsidered, in terms of configuration and function, as the arrangementin series of two decoupling modules as described above.

FIGS. 7A and 7B show a monolithic device according to a third embodimentof the invention. The main differences from the device 10 concern thetriangular directrices of the resonator R″ and of the hollow cylinder2″, and the nature of the material, the device 30 being formed in a flatplane of quartz parallel to the crystallographic plane XY, where X isthe electrical axis and Y is the mechanical axis. The choice of quartzis useful if a low manufacturing cost is a decisive criterion. Thus thedevice 30 may be formed by combined chemical machining of a quartz plateby a method similar to that used in the clockmaking industry formanufacturing quartz crystals for watches. In most cases, chemicalmachining of quartz, generally carried out in a bath containinghydrofluoric acid, causes the appearance of oblique facets for whichallowance must generally be made. In order to make the resonator R″produced by chemical machining resemble a right cylinder, the directrixof the cylinder must be an equilateral triangle whose sides are parallelto a mechanical axis Y. It should be borne in mind that the trigonalcrystal lattice of quartz means that there are three X axes in thecrystallographic plane XY, spaced at angular intervals of 120°, andthree Y axes spaced at equal angular intervals of 120°. It should alsobe borne in mind that the chemical machining of a side parallel to the Yaxis, when the material to be removed is on the negative side of thecorresponding X axis, is carried out virtually perpendicularly to theplane XY until the bottom of the etch is reached, in other words withpractically no oblique facets.

Thus, the resonator R″ and the external cylindrical surface of thehollow cylinder 2″ are right cylinders. On the other hand, the internalcylindrical surface 2″ is in the shape of a truncated cone with atriangular directrix, as shown in FIG. 7B. This is not a drawback forthe operation of the device 30 if this shape is allowed for in thedigital simulations used to optimize the design of the device. Personsskilled in the art will understand that the expression “right cylinder”,as used here, is to be considered in the wider sense, the importantrequirement being that the operation of the device 30 is similar to thatof the device 10 described above, and that the device 30 may be attachedto an attachment area ZF″ located on the external surface of the hollowcylinder, this area ZF″ being virtually decoupled from the vibration ofthe resonator.

FIGS. 8A and 8B show a device 40 according to a fourth embodiment of theinvention. The main differences from the device 10 concern the squaredirectrices of the resonator R′″ and of the hollow cylinder 2′″, and thenon-monolithic nature of the device, as the device 40 is formed in anSOI (Silicon On Insulator) plate. More specifically, the SOI plate isformed by two identical flat plates of silicon (Si) mounted on eitherside of a flat plate of silica (SiO₂). Silicon, like silica, is amaterial with very low viscous damping. The mounting of the silicon andsilica plates is generally based on adhesion at the atomic level, whichalso helps to ensure very low viscous damping. The thickness e of thesilica plate is preferably less than a tenth of the thickness of each ofthe silicon plates, in other words less than a twentieth of the totalthickness h of the SOI plate.

The device 40 is formed by plasma machining performed on both faces ofthe SOI plate. The machining parameters are chosen so as to ensure thatthe machining is selective and suitable for strong etching of siliconand weak etching of silica. Thus it is easy to control the depth ofetching in order to stop the machining when it reaches the silica plate,which serves as a stop layer. Thus it is easy to form the device 40 inwhich the membrane 1′″ is made of silica and the resonator R′″ and thehollow cylinder 2′″ are predominantly made of silicon.

Silicon has a cubic crystal lattice. It is therefore generallyadvantageous to prefer the square form for the directrices of theresonator and of the hollow cylinder, the sides of the square beingparallel to the main axes of the silicon, which generally results inbetter operation of the device 40.

With regard to the shape of the directrices of the hollow cylinder inparticular, it may be advantageous, in order to improve the operation ofthe device still further, to avoid using a perfect square, while stillretaining a shape generally resembling a square. This has beendemonstrated by the work done to optimize the geometry of the device 40by digital simulation, the purpose of this work being to ensure that theattachment area ZF′″ is virtually decoupled from the vibration of theresonator. In terms of the feasibility of manufacture, there is noparticular difficulty in machining the optimal shape resulting from thedigital simulations, because the machining mask used for plasma etchingis made by photolithographic methods.

It should therefore be understood that the expression “square directrix”as used herein is to be interpreted in the broad sense, and moregenerally that the shape of the directrices of the hollow cylinder maydiffer substantially from that of the directrix of the resonator.

The devices according to the invention have been described mainly interms of their mechanical behaviour.

Where the method of exciting the vibration of the resonator isconcerned, various means may be used.

For example, for the quartz device 30 of triangular shape, electrodesdeposited on the machined sides of the hollow cylinder may be used togenerate an electrical field along the electrical axis X, thiselectrical field being coupled by the piezoelectric effect to thealternating compression and extension of the thickness of the wall ofthe hollow cylinder.

Also by way of example, for the silica devices 10 and the SOI device 40,metal sheets or mirrors placed on the faces of the resonator flush withthe faces of the plate may be used to excite the vibration of theresonator by an electrostatic effect or by an optical effect such as aphotothermal effect or by radiation pressure. Since these faces of theresonator are subjected to virtually no mechanical deformation, butsimply an alternating translation during the vibration of the resonator,the metal sheets and mirrors do not in any way alter the quality factorof the resonator, provided that they are placed on the two faces of theresonator so as to preserve the equilibrium of the masses.

1. A device including a resonator and a mechanical decoupling module,the resonator being formed by a right cylinder vibrating inextension/compression mode along its central longitudinal axis andhaving a vibration node in its mid-plane which is perpendicular to thelongitudinal axis, the vibration naturally inducing radialextension/compression deformations, characterized in that the decouplingmodule includes a hollow right cylinder surrounding and spaced apartfrom the resonator and having its central longitudinal axis and itsmid-plane coinciding with those of the resonator, and a membranepositioned in the mid-plane and rigidly connected to the cylindricalsurface of the resonator and with the internal cylindrical surface ofthe hollow cylinder, and in that the hollow cylinder vibrates inextension/compression mode along its longitudinal axis in antiphase withthe vibration of the resonator, as a result of which the effects of theradial deformations of the hollow cylinder and of the resonatorcompensate each other in an area located on the external surface of thehollow cylinder close to the mid-plane.
 2. A device according to claim1, characterized in that it comprises an additional right hollowcylinder surrounding and spaced apart from the aforesaid hollow cylinderand having its central longitudinal axis and its mid-plane coincidingwith those of the resonator, and an additional membrane positioned inthe aforementioned mid-plane and rigidly connected to the externalcylindrical surface of the aforesaid hollow cylinder and to the internalcylindrical surface of the additional hollow cylinder, and in that theadditional hollow cylinder vibrates in extension/compression mode alongits longitudinal axis in antiphase with the vibration of the aforesaidhollow cylinder.
 3. A device according to claim 1, characterized in thatit is formed in a flat plate of material, the thickness dimension of theplate lying on the longitudinal axis of the resonator.
 4. A deviceaccording to claim 3, characterized in that the device is monolithic,and in that the material is an isotropic material with very low viscousdamping, such as silica, and in that the directrices of the resonatorand of the hollow cylinder are circular in shape.
 5. A device accordingto claim 3, characterized in that the device is monolithic, in that thematerial is quartz, the plate being parallel to the crystallographicplane XY, and in that the directrices of the resonator and of the hollowcylinder are in the shape of an equilateral triangle each of whose sidesis parallel to a Y axis.
 6. A device according to claim 3, characterizedin that the plate is a plate of SOI, and in that the directrices of theresonator and of the hollow cylinder are in the shape of a square whosesides are parallel to the main axes of the silicon.
 7. A deviceaccording to claim 2, characterized in that it is formed in a flat plateof material, the thickness dimension of the plate lying on thelongitudinal axis of the resonator.